Smoothed fit

The algorithm originally proposed by Moody and Darken (1989) uses >means clustering to determine the centers of the clusters. The hypersphere around each cluster center is then determined to ensure sufficient overlap between the clusters for a smooth fit by criteria such as the P-nearest neighbor heuristic,... 

The optimal mutation rate is strongly influenced by the finite number of mutants that can be screened. A smooth fitness landscape implies that many mutations can be accumulated without disrupting the fitness. 

The staircase function N E) is interpolated by a mean staircase M E), a smooth fit to the actual staircase function N E). The mean staircase is shown as the full fine interpolating the steps in Fig. 4.1. The mean staircase allows us to define the mean level density p E) as... 

Figure 17 Time series of AOT (top) and Angstrom exponent (bottom) at the Department of Energy Atmospheric Radiation Measurement site in North Central Oklahoma over the period 1993-1999. Measurements are by sun-photometry. The points represent daily averages the curves are smooth fits of the data to guide the eye (Michalsky et aL, 2001) (reproduced by permission of American Geophysical Union from /. Geophys. Res. 2001,106, 12099-12107).

Figure 3 Krypton isotopes in solar system volatile reservoirs, plotted as %o deviations of the ratio to Kr, and normalized to the ratio in terrestrial air (Basford et al., 1973). The heavy solar Kr cruve represents a smooth fit to the measrued solar-wind isotope ratios. Measured SW-Kr from Wieler and Barn" (1994) and Pepin et al. (1995) Mars Kr from Pepin (1991) carbonaceous chondrite Kr from Krummenacher et al. (1962), Eugster et al. (1967), and Marti (1967) (Pepin and Porcelli, 2002) (reproduced by permission of the Mineralogical Society of America from Rev. Mineral.

Figure 31. Representative data showing OH formation following 236 nm CO2-HI excitation. The ordinates in (a) and (b) are the Qi,(l) and Qi,(6) LIF signals, respectively, while the abscissa is the delay time. The dashed curve is the response function of the laser system. The solid curves are the calculated best fits, assuming a two-parameter description for the time dependence of OH formation the best least-squares fits yielded (a) t, = 0.9 ps and Tj = 1.9 ps, and (b) x, = 0.7 ps and Xj = 1.1 ps (see Table 4). The points at the top are the residuals between the experimental points and the smooth fit. From Ref. 43 with permission of the Journal of Chemical Physics.

The eleetrie field EJ x) can be dedueed from a differentiation of the smooth fitting frinetion displayed in Figure 20.2a, revealing rather large eleetrie fields... 

It is advisable to wear smooth-fitting protective disposable gloves while working with alkali metals and strongly basic reagents. 

Apply an adjustable gas pressure to a smooth-fitting ball bearing piston Apply a constant displacement and measure force with a load cell (a universal testing machine fitted with a compression jig can be used). 

Finally, it should be mentioned that sandwich formation is not a privilege of crown ether complexes with metal ions displaying ionic radii which are too large to fit into the ligand cavity. Infrared spectroscopic studies revealed thatbenzo[15]crown-5 forms a 2 1 sandwich with Na (which could smoothly fit into the cavity), if the anion is tetraphenyl borate This is due to the inability of the anion to provide donor atoms for the Na ion which thus requires a second crown for a sufficient coordination. 

Figure 10.10 shows the pressure dependence of Tc for Ce in comparison to thorium. Th is below Ce in the periodic table at the beginning of the 5f series. It is therefore the most reasonable element for a comparison. The pressure dependence of Tc for Th has been previously determined by Fertig et al. (1972). As seen from fig. 10.10, Tc steeply decreases up to 50 kbar. Around 75 kbar it passes a shallow minimum. Above 110 kbar Fertig et al. observed again a small decrease of Tc. The curve shown for Ce is a smooth fit of the data of fig. 10.8. We think there is a striking similarity to the Tc-P curve of Th. The peculiar shape of the curves deserves further study. 

Fig. 10.12. vs. pressure for lutetium. The numbers indicate the sequence of 11 measurements for one particular sample. As seen, is a reversible function of pressure. Two arrows indicate that no superconductivity was detected at those pressures down to — 20 mK. The curve is a smooth fit of the data (Probst, 1974). 

The seamless technique is pioneering in apparel markets because of its smooth fit, comfort, invisibUity, and easy care properties. Seamless knitting machines have the... 

FIG. 4. Variation of the birefringence factor a as a function of temperature at 6328 A for the mixture of cholesteryl chloride and cholesteryl myristate (1.75 1 by wieght). The solid curve is a smooth fit to the data points. 

FIG. 9. Phase-matching peak for mode combination 2 observed with a sample 130 Mm thick. The circles are experimental points with an uncertainty of 20%. The curve is a smooth fit to the data. 

Figure 4. Adsorption/desorption isotherm for a porous HSQJitm and a series ofMSQ films formulated with varying amounts ofporogen. The solid lines are smooth fits using the sum of a sigmoidal and lognormal curve. The standard uncertainty in rAe tqrtake is on the order of (6 to 7) %.

Figure 5. Approximate pore size distributions from the smooth fits through the isotherms in Figure 4 (Eq. (1) used to convert P/Po into a pore size). The distributions from the adsorption branch (dotted lines) are always broader and shified to larger pore sizes than the corresponding desorption branch.

Of course, this proposed picture may not be the only one possible. However, it is interesting to note that not only is it able to explain "naturally all major features of the infrared emission from HII regions, but, quite amazingly, it also provides a smooth fit to the properties of the dust in interstellar space. 

An iterative solution of Eq. 15 then yields Eb (%iax)- H proved difficult to accurately fit Eq1 (9) to a polynomial in ic, however an accurate (smoothed) fit was possible using cubic splines. This fitted barrier function will be denoted Eq1 s (9)... 

Whether DLS, DWS, Mie scattering, or other applications in which unfractionated samples are analyzed, the resulting distributions produced by modern instruments, while frequently facile to obtain and neat in appearance, must be treated with caution, as there is usually a large amount of data smoothing, fitting, and assumptions applied in using inverse Laplace transform and several other commonly employed methods. The best means of finding distributions of size and mass continue to be fractionation methods, such as SEC [32-34], field flow fractionation (FEE) [35-37], capillary electrophoresis [38], capillary hydrodynamic fractionation [39], and so on. 

Figure 78 shows a plot of the soft mode and Goldstone mode rotational viscosities measured on either side of the phase transition between the smectic A and SmC. It can be seen that, except in the vicinity of the phase transition, the viscosity seems to connect fairly well between the two phases. The activation energies of these two processes are, however, different. This result may be compared to results obtained by Pozhidayev et al. [148], referred to in Fig. 67. They performed measurements of y beginning in the chiral nematic phase of a liquid crystal mixture with corresponding measurements in the SmC phase, and have shown the viscosity values on an Arrhenius plot for the N and SmC phases. Despite missing data of y in the smectic A phase they extrapolate the N values of y down to the smectic C phase and get a reasonably smooth fit. Their measurements also show that y is larger than y, and this is universally the case.

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